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Chapter 4: Q. 4.142 (page 550)

Write the inequality shown by the shaded region in the graph with the boundary line 3x鈭�y=6

Short Answer

Expert verified

The inequality shown by the graph is 3x-y鈮�6.

Step by step solution

01

Step 1. Given Information

We are given an equation 3x鈭�y=6and a graph,

02

Step 2. Finding the inequality 

The line 3x鈭�y=6is the boundary line. On one side of the line are the points with3x鈭�y>6 and on the other side of the line are the points with 3x鈭�y<6.

Checking the inequality with point 0,0,

role="math" 3x鈭�y>63(0)鈭�0>60>6

False.

03

Step 3. Finding the inequality 

Checking the inequality with point 0,0,

3x鈭�y<63(0)鈭�0<60<6

True.

Since 3x-y>6is false for (0,0)which is not the part of shaded region, hence shaded region is the solution for the inequality role="math" localid="1647585928644" 3x-y>6

Also, the boundary line is graphed with a solid line, the inequality includes the equal sign.

3x-y鈮�6

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Most popular questions from this chapter

In the following exercises, find three solutions to each linear equation.

x+y=鈭�2

In the following exercises, which ordered pairs are solutions to the given equations :

y=12x-1

(a) 2,0(b)-6,-4(c)-4,-1

Which of the following ordered pairs are solutions to the equation4x-y=8?

(a)(0,8)(b)(2,0)(c)(1,-4)

Plot each point: 鈸� (4, 0) 鈸� (鈭�2, 0) 鈸� (0, 0) 鈸� (0, 2) 鈸� (0, 鈭�3) .

Find the intercepts for3x-2y=12
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